This is a pretty good idea.
I would also suggest adding an option in Preferences to turn the messages off. Also, have them turn off automatically after the team has played it's first full season and send an e-mail at that time explaining how to turn them back on if desired.
The only message I would probably turn off quickly is my trainer telling me to train specific guys. I know who I want to train and don't need my trainer to tell me. A hint as to who is close to popping would be nicer, I think, if he sent it after the weekly training was done. Like an e-mail that says "A little more training in Pressure and Robert Bellamy will definitely see the benefit" would be nice so I would have an idea if another week would get that pop or if I am going to be frustrated with another week and no pops.